# Open Problems Kernel

## Purpose

This document is the open-problems source text for the `j3_oc` branch.

Its job is to keep the branch honest about what it still owes.

This is not a weakness. It is the branch-control system.

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## Scope

This file covers:

- unresolved reduction problems
- unresolved questions about `u`
- unresolved questions about `SU(3)`
- unresolved questions about mixing
- unresolved questions about observables and falsification

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## Main open-problem cluster

The branch's open problems cluster around six linked tasks:

1. ambient-to-observable reduction
2. status of `u`
3. structural versus physical `SU(3)`
4. geometric meaning of mixing
5. explicit observable / measurement language
6. decision criteria relative to `J3(O)`

These are not separate loose ends. They are the branch's actual center of gravity.

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## Open problems by domain

### Statics

- what real, Hermitian, or positive sectors are admissible inside `J3(C \otimes O)`?
- can `u` arise from ambient structure rather than direct insertion?
- does the complexified branch offer a cleaner route to `SU(3)` than the real branch?

### Dynamics

- what are the fundamental evolving objects of the ambient branch?
- what counts as interaction before reduced effective models are introduced?
- can mixing be defined geometrically rather than imported from `spin2_3`?

### Epistemics

- what exactly are the reduced states?
- what exactly are the observables?
- what operation counts as measurement on the observable slice?
- why this observable slice rather than another?

### Consistency

- does the complexified branch earn anything essential over `J3(O)`?
- can reduced `Spin(2,3)` structure be obtained without ad hoc inserts?
- are the reductions disciplined or selectively chosen?

### Interpretation

- what physical meaning, if any, does complexification really carry?
- is the ambient object ontic, generative, or partly redundant?
- when does branch interpretation outrun branch derivation?

### Phenomenology

- what would count as an observable consequence specific to `j3_oc`?
- what would differ from `J3(O)` or `spin2_3` if the branch succeeded?

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## Priority ordering

The current priority order should be:

1. make the reduction map sharper
2. decide the strongest available status of `u`
3. sharpen the `SU(3)` story from structural to physical or admit the gap
4. define mixing geometrically
5. define states, observables, and measurement
6. maintain branch-level decision and falsification criteria

This is the efficient build order for the branch.

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## Open-problem ledger

| Problem | Domain | Severity | Comment |
|---|---|---|---|
| ambient-to-observable reduction is not yet explicit enough | cross-domain | high | main missing-middle burden |
| the status of `u` remains unresolved | statics / interpretation | high | central branch test |
| structural `SU(3)` has not been connected to physical color | statics / consistency | high | major bridge debt |
| mixing is not yet geometrically defined | dynamics / interpretation | high | branch-specific obligation |
| states, observables, and measurement are only provisionally defined | epistemics | high | needed for physical clarity |
| the branch has not yet shown why complexification is needed over `J3(O)` | consistency | high | main comparative burden |
| reduced `spin2_3` structure is not yet derived from this branch | cross-domain | high | major proof burden |
| branch-specific phenomenology is not yet mature | phenomenology | high | expected at this stage |

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## Working bottom line

The `j3_oc` branch already has a coherent purpose, but not yet a complete theory.

Its core debts are:

1. reduction
2. direction
3. color
4. mixing
5. observables
6. comparative justification

If those are strengthened, the branch becomes physically competitive.

If they are not, the branch should remain in controlled exploratory status.